Solve \frac{\cos x}{1+\sin x}+\frac{1+\sin x}{\cos x}=2

Emmanuella Browne

Emmanuella Browne

Answered question

2022-02-27

Solve
cosx1+sinx+1+sinxcosx=2

Answer & Explanation

besplodnexkj

besplodnexkj

Beginner2022-02-28Added 7 answers

2=cosx1+sinx+1+sinxcosx
=cos2x+(1+sinx)2cosx(1+sinx)
=cos2x+sin2x+1+2sinxcosx(1+sinx)
=2+2sinxcosx(1+sinx)
=2(1+sinx)cos(1+sinx)
=2cosx
cosx=1, x=2kπ

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